A. Field of the Invention
The present invention relates to an image displaying method for use in computer graphics and, more particularly, to a method for displaying luminance to obtain an image expressing glossiness of a surface of an object and/or a method for designating a color of the image.
B. Prior Art
In the technical field of computer graphics, a shading treatment is generally applied to an image of an object to be displayed so that texture of the surface of the object may be represented.
Except where all or part of the light incident on an object is transmitted through the object, that is where the object is lucent or transparent, representation of object surface texture depends on representing diffusedly reflected light and specularly reflected light.
Further, in practice, a method for calculating the luminance at points on the object's surface which accounts for ambient light greatly contributes to the representation of surface texture.
Generally, when a shading is used to represent texture the calculation of the luminance on the object's surface is performed according to an illumination model expression.
A simple and easily calculable illumination model expression is known in the art, a first term accounting for ambient light and a second term accounting for diffusedly reflected light according to Lambert's Cosine law. That is, ##EQU1## where I: luminance at a point on the surface of an object
k.sub.a : reflection coefficient of ambient light, EQU (0.ltoreq.k.sub.a .ltoreq.1) PA1 I.sub.a : luminance of ambient light PA1 k.sub.d : diffuse reflection coefficient PA1 I.sub.j : luminance of the jth light source, EQU (0.ltoreq.j.ltoreq.m, 0.ltoreq.I.sub.j .ltoreq.1) PA1 .theta..sub.j : the angle formed between a direction vector Lj of the jth light source and a normal vector N at the point (refer to FIG. 11). PA1 : index representing expanse of specularly reflected light. In particular 1.ltoreq.n, and the larger the value of n, the more spotlight-like is the specularly reflected light PA1 .alpha.j: an angle formed between the jth specularly reflected light vector (i.e., the reflection of the jth light-source direction vector across the normal vector N at the point) L.sub.j and a visual-point direction vector E (refer to FIG. 12 ).
However, since glossiness of an object is produced by specularly reflected light, the texture of a glossy surface of an object cannot be represented safely by the luminance expression expressed above.
An expression for representing the texture of a glossy surface of an object, is known in the art (2), which is obtained by adding to the expression (1) an experimental model expression for specularly reflected light by Bui-Tuong-Phong. That is, ##EQU2## where ks: specular reflection coefficient EQU (ks=1-kd, 0.ltoreq.k.ltoreq.1)
In computer graphics, the color of the surface of an object is represented by a combination of three numerical elements. Some of these three-element representations are known in the art as RGB (Red, Green, Blue), HSV (Hue, Saturation, Value ), and HLS ( Hue, Lightness, Saturation).
By representing a color by a combination of three numerical elements as described above, color designation of a displayed image can be made by introducing a concept of a three-dimensional body (color cube) with the three numerical elements being designated along the body's three coordinate axes.
For example, a color of RGB representation becomes a cube having R, G, and B, respectively as the axes as shown in FIG. 13. With such an RGB cube, neutral colors (white-gray-black) exist in a diagonal connecting the point of black to the point of white.
With a hexagonal pyramid three element representation, having the diagonal of the color cube of the above described RGB representation, where neutral colors exist and are used as the axis of the value, a hexagonal-pyramid color cube of HSV representation as shown in FIG. 14 is obtained.
When the above described color cube of HSV representation having the point of black as its vertex is further developed into a bicone having the points of black and white as its vertices, a color cube of HLS representation as shown in FIG. 15 is obtained.
Color designation of an image to be displayed graphically has conventionally been made by designating three elements individually. For example, as shown in FIG. 16, by having the circular display area AR.sub.1 provided for displaying H (hue), a horizontal strip area AR.sub.2 below the hue display area AR.sub.1 provided for displaying S (saturation), and a horizontal strip area AR.sub.3 below AR.sub.2 provided for displaying L (lightness), the color designation of an image to be displayed may be made by individually designating H (hue), S(saturation), and L (lightness) on display areas AR.sub.1, AR.sub.2, and AR.sub.3 respectively. Further, a hue display for fine adjustment of H (hue) may be provided in the vertical strip area AR.sub.4 to the right-hand side of the hue display area AR.sub.1 so that a fine adjustment of H (hue) can be achieved by designating a fine adjustment of hue on display area AR.sub.4.
Further, in applying a shading treatment to a displayed object in computer graphics, a process as for changing only the lightness (luminance) of a color designated by an HSV representation or an HLS representation is known in the art.
If in applying a shading treatment to an image of an object to be displayed to thereby express texture of the surface of the object as described above, the calculation of luminance on the surface of the object is performed in accordance with an illumination model expression which considers only ambient light and diffusedly reflected light glossiness of the surface of the object, produced by specularly reflected light cannot be taken into account. Further, even if an illumination model expression with ambient light, diffusedly reflected light, and specularly reflected light taken into consideration is employed to express the glossiness of the surface of the object, a difficulty arises in that it takes a very long time to calculate the expression values.
Besides, with prior art techniques, although only V or L may be changed with H and S kept unchanged for color designations made by HSV representation or HLS representations respectively, the original color designation of the displayed image has nevertheless been made by individually designating the three elements as described above, and therefore vast amounts of labor and time are expended to designate a desired color.
Therefore it is an object of the present invention to provide a method for displaying an image employing an illumination model expression with only ambient light and diffusedly reflected light taken into consideration, but being capable of representing surface glossiness.
Another object of the present invention, is to provide a method of image of color designation which may be performed simply and quickly .